Question 108
A ray emanating from the vertex $A$ of the triangle $ABC$ intersects the side $BC$ at $X$ and the circumcircle of $ABC$ at $Y$. Prove that
$$
\frac{1}{AX} + \frac{1}{XY} \geq \frac{4}{BC}.
$$
$$
\frac{1}{AX} + \frac{1}{XY} \geq \frac{4}{BC}.
$$